This study aims to investigate the impact of observation error correlations and non-orthogonal observation operators on analysis accuracy using a chaotic dynamical model known as the Lorenz-96 40-variable model, extending the previous study by Miyoshi et al. using a simple two-dimensional conceptual model. The results corroborate Miyoshi et al.'s conceptual study and show that the analysis is more accurate when the row vectors of a linear observation operator are correlated positively (negatively) with negatively (positively) correlated observation error. The online estimation of the observation error covariance matrix based on the Desroziers diagnostics is successful when we have reasonable a priori knowledge about the observation error correlations.